I am working on building a physics model into the xStats home run prediction. In order to do so, I had to learn the equations backwards and forwards. I started with Alan Nathan's calculator as a starting point. I studied it, took notes, memorized it, and created my own version from memory. The result of which you can see below. It is functionally identical to Alan Nathan's calculator with one major difference: it doesn't use wind.

I've also added a few other features that Nathan's calculator does not have. Let me show you its features.

Select a ballpark. This will Automatically input an elevation. You can search by team or ballpark and it will work either way.

Initial conditions for a batted ball. You should be most interested in the first three: Exit Velocity, Launch Angle, and Spray Angle. You can edit all of the rest if you'd like. Remember elevation is automatically changed by the ballpark.

Target Wall Height. The calculator will indicate the point in the trajectory where a ball crosses the height specified. (See 8. Below).

You can input a known wall distance and wall height and it will be drawn on the chart. (See 9. Below).

The distance from home plate at the specified target height. There are three results. The red line depicts the upper range for coefficients of drag and lift. The blue result uses the mean values for drag and lift. The green line uses the lower range for drag and lift.

Vertical and horizontal angles are drawn for reference.

Various constants and other values used for calculation. Do not edit these.

Each painted trajectory will have a small vertical line showing where it crosses the target height (See 3. Above).

The thick black line shows the location for the inputed Real Wall (See 4. Above).

Calculations. You don't need to worry about these, but you can look at them if you'd like.

I took the upper and lower coefficients from a few studies into baseball coefficients of drag and lift. I was hoping they would approximate the second or third standard deviation, but in my testing I have found that actual MLB batted ball distances have an even wider range than depicted by this calculator.

The difference could be due to wind, I cannot rule that out. I find it hard to talk about wind at all, since it is such a complex issue within a baseball stadium. It swirls around the stadium in difficult to predict, chaotic patterns. Small changes in wind speed or direction can create large changes in the local wind effects at any given point within the park. Wind is difficult, and I'm choosing to ignore it for the moment.

At the end of the day, this calculator is a first step towards the greater goal of integrating a physics model into home run prediction. You can mess around with the spreadsheet as you please. Just open the link below and click File -> Make a Copy.

Trackman radar currently measures around 88 to 90% of all batted balls. I wrote a piece for The Hardball Times outlining this issue which you can read here. In the spreadsheet below you can find the appendix for that Hardball Times piece, including which batted balls you may wish to exclude from your own calculations.

As you can see, Dribble balls are very consistent from one year to another. Pop ups are pretty solid, as are flyballs. The Groundball, Line Drive, and High Drive groups are not nearly as stable. Realistically, all three of these groups are very fungible, and batters may slide between each group pretty fluidly.

The purpose of these categories is not to predict what a batter may do in the future, but rather to describe what he has done in the past. If a batter is very successful due to a large number of High Drives, you should be very suspicious. You should generally expect to see random noise out of these three battle ball types, and analyze player changes over time from that perspective.

Below I have an attached spreadsheet showing the changes each player displayed between 2016 and 2017. Keep the above year to year correlations in mind when sifting through this data.

Sometime in late 2015 the baseballs used by Major League Baseball appear to have changed. How they may have changed and whether it was intentional are hotly contested topics. Regardless of how you feel on the topic, the baseball appears to be traveling five to six feet further now than it did prior to this change.

This flight can be converted to a change in effective velocity, since the ball travels around five additional feet for each additional mile per hour. Meaning the ball has an effective velocity about 1 to 1.2 miles per hour faster than what is registered. Meaning, in order for a ball from the first half of 2015 to fly as far as a ball hit in 2016 or 2017, it would need to have been hit about one mile per hour faster.

You can reverse this logic and say that subtracting a mile per hour from a ball hit in 2016 or 2017 would roughly approximate where it would have landed when using the older baseball. I have run Back in October, after the season had concluded, I ran xStats on a dataset which did just this: it subtracted a mile per hour from the balls hit in 2016 and 2017 and calculated their success rates. You can see the results in the attached spreadsheet.